What is the derivative of #f(x)=sin(log_2(x))# ? Calculus Differentiating Logarithmic Functions Differentiating Logarithmic Functions without Base e 1 Answer Wataru Sep 22, 2014 By Chain Rule, #f'(x)=cos(log_2x)cdot1/{(ln2)x}={cos(log_2x)}/{(ln2)x}# Note: #(log_bx)'=1/{(lnb)x}# Answer link Related questions What is the derivative of #f(x)=log_b(g(x))# ? What is the derivative of #f(x)=log(x^2+x)# ? What is the derivative of #f(x)=log_4(e^x+3)# ? What is the derivative of #f(x)=x*log_5(x)# ? What is the derivative of #f(x)=e^(4x)*log(1-x)# ? What is the derivative of #f(x)=log(x)/x# ? What is the derivative of #f(x)=log_2(cos(x))# ? What is the derivative of #f(x)=log_11(tan(x))# ? What is the derivative of #f(x)=sqrt(1+log_3(x)# ? What is the derivative of #f(x)=(log_6(x))^2# ? See all questions in Differentiating Logarithmic Functions without Base e Impact of this question 3279 views around the world You can reuse this answer Creative Commons License